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Encipher the following message using the key 19, 15, 22:

there is a secret passage behind the picture frame

Answer:

To do this, start by representing each letter of your plaintext by a number from 0-25 ('a' = 0, 'b' = 1, ..., 'y' = 24, 'z' = 25). Do the same for your key (unless, as in this case, it is already given by numbers). Then, write out the key over your plaintext just like you did for the letter-key. Finally, add the two numbers in each column. If this number is between 0 and 25, write down the corresponding letter. If it is bigger than 25, simply subtract 26 from that and write down the letter that corresponds to the number you get. Here's the first part of the example worked out:

"there is a secret passage" becomes:

19 07 04 17 04 08 18 00 18 04 02 17 04 19 15 00 18 18 00 06 04

We then write out the key repeatedly and put the message underneath:

KEY: 19 15 22 19 15 22 19 15 22 19 15 22 19 15 22 19 15 22 19 15 22
MES: 19 07 04 17 04 08 18 00 18 04 02 17 04 19 15 00 18 18 00 06 04
--------------------------------------------------------------
SUM: 38 22 26 36 19 30 37 15 40 23 17 39 23 34 37 19 33 40 19 21 26
-26: 12 22 00 10 19 04 11 15 14 23 17 13 23 08 11 19 07 14 19 21 00
LET: _M _W _A _K _T _E _L _P _O _X _R _N _X _I _L _T _H _O _T _V _A

The whole answer is:

MWAKTELPOXRNXILTHOTVAUTDBCZMWAIXYMJNXUNTBA